2008 Toyota Yaris Stalling

I have a 2008 Toyota Yaris S Sedan. I’ve had it for 5 years, and it currently has 63,000 miles. About 3 years ago, it started stalling out while I was driving. It was only occasional, but it soon got worse and more frequent.
First problem: It would stall out when I would drive 35 MPH or under when it was 20 degrees or colder or when parked in direct sun. It would stall while driving and after I stopped or in Park
Second Problem: It would stall out when I would drive 70 MPH or under, while driving, no matter the weather conditions.
Third Problem: On cruise control, the car would loose speed and drop down to 50 MPH then leap forward and speed up to 90-95 MPH before settling back on 73 MPH.
Fourth Problem: It jerks while driving. It’ll start to stall, then speed up, then start to stall, then speed up, repeat once more then speed up.
Fifth Problem: When the first three problems occurred, the car would shake during and after.

I’ve taken the car in seven times to two different Toyota dealerships, with nothing found. They were able to recreate the stalling issue, but none of the others. I contacted the Toyota company and they opened an inquiry, but found nothing and closed the case. I need this car to last me a couple more years.

Any ideas as to what the problem could be and if it’s fixable?

Do you ever get a check engine light when this is happening? Even if you don’t, has anyone checked for codes? The best time to check is when this condition is occurring, even if the CEL doesn’t come on.

The light does not come on. I went to AutoZone when it first started happening and they checked, but nothing came up. I’ve tried to take it in right after it has happened, but by the time I get to the dealership, the issue “disappears”.